General comments:

The manuscript designed a self-supervised fusion method based on spatiotemporal Discrete Cosine Transform to fuse sparse satellite data and global full-coverage GHGs reanalysis data for the seamless estimation of long-term daily global XCO₂ and XCH₄. It is an interesting study, especially for providing long-term XCO₂ and XCH₄ datasets that don’t need any auxiliary variables and analyzing the global pattern of XCO₂ and XCH₄ trends. I think the paper needs minor revision before acceptance for publication. Following are some detailed comments:

Specific comments:

1. The assessments of spatial distribution on a daily temporal scale may be necessary for a daily dataset.
2. Satellite XCO₂ of 2010-2014 and 2015-2020 come from two datasets. It is crucial for users who rely on the long-term dataset to assess the sensitivity difference between various data. Did the authors compare the difference between the two datasets, and was this difference either ignored or corrected for ?
3. I have some questions that are not addressed in the Methodology section. What are the range and meaning of M, N, and P in line 175? while u, v and w have the same range as i, j and t. what’s the difference and relationship between them?
4. In the Equation 4, 𝛿 represents a series of values or a three-dimensional tensor. Based on Equations 5 and 6, it appears that 𝛿 is a tensor. How are positions without values in 𝛿 handled and does it affect the final iteration process?
5. I am curious that the configuration of the parameters in line 208. How do these parameters affect the results, especially for 𝜀?

Technical corrections:

L21: The full name of 𝜎 and R²

L21-22: Why the R² of XCO₂ against TCCON measurements is given as a range, while the R² of XCH₄ is a single number? They should be consistent.

L117: The full name of QA. It is the first mention in this text.

L349: R²: 0.91 or 0.95 means the results of GOSAT and OCO-2? This sentence can be expressed more clearly.

Figures: Modify the superscript of R₂ and subscript of XCO₂ and XCH₄ in all Figures.

Text: Figure and Fig. need to be unified.

References: Modify the subscript of all references.

L529: 108 000 European cities.

This study describes an effective approach to generate global long-term seamless XCO₂ and XCH₄ based on a self-supervised fusing method from OCO-2, GOSAT, and CAMS-EGG4. Generally, this paper is well organized and written, of which the methodology, validation techniques, and experiment results are reasonable. However, some details are unclear and several issues are required to be modified before this paper being published in ESSD. A major revision is recommended. Specific comments are listed as follows.

Major comments:

1. P9L202, Eq. (6): Is it possible to visualize intermediate results of STDCT? The visualization of intermediate results of STDCT can help understand this procedure.
2. P9L205, Eq. (7): I notice that the power of the subitem in the denominator is 1, which is different from that in the given references, such as Garcia (2010).
3. Please present the whole formula derivation processes from Eq. (5) to Eq. (6).
4. P9L209: Different initializations of may lead to different final results. Please provide a brief discussion.
5. Will the data completeness of XCO₂/XCH₄ from OCO-2/GOSAT affect the accuracy of final fused results? More data should imply more usable information. Please provide a brief discussion.
6. The data of XCO₂/XCH₄ from OCO-2/GOSAT is extremely sparse in some regions, I wonder if the performance could be improved after fusion under this condition.
7. Table 3-5: The metrics of the individual in-situ validation do not exceed those of CAMS-EGG4 for a few stations after fusion. What could be the potential reasons? Please provide a further discussion.

Minor comments:

1. P5L121: The authors did not consider the latest XCO₂ from OCO-3 for fusion. What is the reason?
2. P5L130: Similarly, the authors also did not adopt the popular XCO₂ from Carbon Tracker for fusion.
3. The figures in the Supplement are too many to follow, which are unnecessary. Table 3-5 have summarized their metrics.
4. Table 3-5: It's better to abbreviate “CAMS-EGG4” into “CAMS” instead of “CE”, which is consistent with other texts
5. Future works and limitations are missing in the Conclusions.
6. Is it feasible to acquire global seamless XCO₂ and XCH₄ only from OCO-2 and GOSAT based on the proposed method?

Reference:

Garcia, D.: Robust smoothing of gridded data in one and higher dimensions with missing values, Computational Statistics & Data Analysis, 54, 1167–1178, 2010.